I am not the best person to comment on this as I have been married for 20 years and so have never had to live through the whole modern dating scene, but I think the problem with your idea is that MB personality types are not equal distributed between men and women. This is likely the reason why you have trouble finding someone on your mental wavelength.
The bigger problem in my opinion is crazy/damaged people. If you could find a way of screening out the crazies via AI you would have a major hit.